Question: Solve for $x$ and $y$ using elimination. ${-x-4y = -31}$ ${x-5y = -23}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-9y = -54$ $\dfrac{-9y}{{-9}} = \dfrac{-54}{{-9}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-x-4y = -31}\thinspace$ to find $x$ ${-x - 4}{(6)}{= -31}$ $-x-24 = -31$ $-x-24{+24} = -31{+24}$ $-x = -7$ $\dfrac{-x}{{-1}} = \dfrac{-7}{{-1}}$ ${x = 7}$ You can also plug ${y = 6}$ into $\thinspace {x-5y = -23}\thinspace$ and get the same answer for $x$ : ${x - 5}{(6)}{= -23}$ ${x = 7}$